#### by Dusa McDuff

Andrew Ranicki (born 30 December 1948, London, and died 21 February 2018, Edinburgh) spent his early years with his parents in Poland and Germany. Later, after a few years at school in Canterbury, he went to Trinity College, Cambridge, where he graduated with a BA in 1969, and a PhD in 1973 under the supervision of Frank Adams and Andrew Casson. A Research Fellow at Trinity College during 1972–77, he spent the next five years at Princeton University, before taking up a Lectureship in the Department of Mathematics at Edinburgh University in 1982. He worked at Edinburgh for the rest of his career, being appointed as Professor of Algebraic Surgery 1995–2016.

Andrew wrote seven influential books on various aspects of surgery theory, as well as some seventy research papers; he organised many conferences both in Edinburgh and in Germany, and supervised eleven PhD students. He (co)edited twelve collections of papers on a wide variety of topics in algebraic topology, as well as working on the editorial boards of many journals. He was very erudite and culturally literate, and curated an imaginative and informative web site (now archived by the University of Edinburgh). Among other honours, he was awarded the Cambridge University Smith prize in 1972, was elected a Fellow of the Royal Society of Edinburgh in 1992, and won the Junior Whitehead Prize in 1983 and Senior Berwick prize in 1994, both from the London Mathematical Society.

When Andrew was promoted to full professor he became professor of Algebraic Surgery. This title was somewhat whimsical; it had to be approved by the Edinburgh Medical School, whose annoyance greatly amused Andrew. However it was also very apt: algebraic surgery was actually a very significant part of Andrew’s contribution to mathematics.

Surgery theory was initiated by Kervaire and Milnor and developed by Browder, Novikov, Sullivan and Wall. It established a method for classifying high-dimensional compact manifolds (a very basic and important class of topological spaces), based on foundational tools from geometric topology, including cobordism theory, vector bundles, and transversality. The resulting “surgery exact sequence” [e1], expresses the classification in terms of homotopy theory and certain algebraically defined surgery obstruction groups.

One of the main themes of Andrew’s work is the exploration of the
borderland between geometry and algebra. An early achievement
[1]
was to show that Wall’s surgery obstruction groups
could be defined as the cobordism groups of algebraic Poincaré
complexes over a suitable ring. This was the origin of a dramatic
reformulation of surgery. Andrew continued to develop and apply the
relevant algebra throughout his whole career, in a series of lengthy
papers and books. This new theory, called algebraic __\( L \)__-theory,
culminated in his 1992 book *Algebraic *__\( L \)__-*Theory and
Topological Manifolds*
[2]
which identifies the geometric surgery exact
sequence entirely in algebraic terms. Many colleagues regard this as
his most influential work.

The flexibility of algebraic Poincaré cobordism, which is defined over
every ring with involution, was essential for establishing Wall’s
“Main exact sequence” (1976) to effectively calculate the surgery
obstruction groups. This method depends on the algebraic __\( L \)__-theory of
localization and completions of rings with involution to reduce
calculations from integral group rings to those over simpler rings.

Algebraic __\( L \)__-theory has a large number of striking applications, most
of which were obtained by Andrew himself, or in collaborations with
colleagues and his PhD students. A brief list of topics indicates the
breadth of these applications:

- Finiteness obstructions and torsion invariants for chain complexes (1985–87)
- Algebraic splitting for
__\( K \)__- and__\( L \)__-theory of polynomial rings__\( A[t,t^{-1}] \)__(1986) - Surgery transfer maps for fibre bundles (1988, 1992)
- Chain complexes over additive categories (1989)
- Lower
__\( K \)__- and__\( L \)__-theory; controlled topology (1992, 1995, 1997, 2003, 2006) - Finite domination and Novikov rings (1995)
- Bordism of automorphisms (1996)
- Circle-valued Morse theory and Novikov homology (1999, 2000, 2002, 2003)
- Noncommutative localization (2004, 2006, 2009)
- Blanchfield and Seifert algebra in high-dimensional knot theory (2003, 2006)
- The geometric Hopf invariant and surgery theory (2016)

As well as developments that arose from his lively interactions with colleagues and coworkers such as Michael Weiss, Wolfgang Lück, Erik Pedersen, Jim Davis, and Ian Hambleton, Andrew’s work has the potential to inspire significant new directions.

Dennis Sullivan
points out that __\( L \)__-theory, which is based on the
Poincaré duality property of manifolds, provides a systematic way to
incorporate duality into a variety of algebraic settings, and this
might help make various longstanding conjectures about manifolds
finally accessible.

Everyone who met Andrew enjoyed his wit, his inexhaustible store of literary anecdotes, and his vivid personality. This was perhaps in large part due to his family background: his father Marcel Reich-Ranicki, after a harrowing escape from the Warsaw ghetto with his wife, eventually became the dominant literary critic in Germany. Marcel was a larger than life celebrity — he was sometimes called the “Pope of German literature” — and Andrew had a presence and laugh to match.

Iain Gordon, reflecting on Andrew’s contributions to department life, writes as follows:

Andrew was an irrepressible spirit in the School of Mathematics who inspired regular visits to Scotland from the very best topologists, often under the banner of Scottish Topology which he helped to run since its foundation in 1981. In addition, he arranged many prestigious seminars, colloquia and events all across the discipline, featuring great mathematicians from throughout the world, including in the last few years Fields Medallists Sir Michael Atiyah, Gerd Faltings, Timothy Gowers and Ed Witten. His house was Edinburgh’s mathematical living room, filled with laughter, gossip, and research highlights. In departmental life, he taught a variety of courses mostly in algebra, geometry, number theory and topology, nearly always exposing the students to quadratic forms and giving them glimpses of the rich mathematical world he inhabited. He was a constant advocate for the use of technology in the School, from email through the internet and onto social media, best illustrated by his monumental and multifarious webpage which is now a permanent resource for mathematicians all over the world.

The following tribute was written by his student Carmen Rovi.

It has been almost a year since Andrew left us, but trying to write about him, I feel I lack the words to express the whirlwind of emotions that his memory brings to me. How was Andrew as an advisor? Andrew was kind-hearted, generous, understanding and above all, he was enthusiastic. His enthusiasm for topology and in particular for surgery theory was a powerful beacon for anyone working in the area and especially for his students. He was able to communicate this enthusiasm and impress onto us his elegant understanding of mathematics.

It is true, and everyone who talked to Andrew will have experienced this at some point, that he would sometimes fall asleep. It is also true that he would then wake up and ask an interesting question or make an insightful comment. The point is that being with Andrew it was impossible to get bored. His sense of humour and hearty laugh combined with a breadth and depth of knowledge not just in mathematics, but also in other areas like music or literature, was always a source of motivation.

Andrew’s lectures were always exciting. Many times he would add a joke or a picture that would help fix an abstract notion in students’ minds. One of his favorites was the picture of the Reverend Robert Walker “Skating on Duddingston Loch” by Raeburn, one of Scotland’s best-known paintings. Looking very closely at this picture one can see that the minister is drawing a figure eight on the ice with his skates. Andrew would use this to give an example of the abstract notion of an element in the fundamental group of the wedge sum of two circles.

When thinking about how Andrew nurtured his students, the beautiful poem by Seamus Heaney Saint Kevin and the blackbird comes to mind. The poem narrates the story of how a blackbird lays her eggs in Saint Kevin’s hand while he is praying and how he patiently protects them until the young are hatched and fledged and flown. And just like Saint Kevin’s prayer, “to labour and not to seek reward” was also part of Andrew’s philosophy: so much effort in putting together interesting projects for his students, so many hours spent guiding us towards our goals and listening to our attempts…he did all this in his selfless, generous manner that we will always treasure in our memory.

Andrew’s generosity of spirit, combined with his wife Ida’s amazing
ability to conjure up magnificent vegetarian meals and imaginative
aperitifs, created convivial gatherings of laughter and great good
cheer. These often took place in their surprisingly sunny garden, a
whole world created by Ida of green beauty, mysterious dense
undergrowth and bright blooms, with inviting little spaces to sit
and chat. Their house was also a marvelously welcoming space for
many mathematicians at all levels, eager students and established
prize-winners, their friends and families included. In later years,
a gift from Marcel (proceeds from the book *Mein Leben* about his
life) allowed them to build a wonderful stone conservatory beside
their house, decorated by a bust of Marcel, a stone frog by the
topologist
Frank Quinn,
and many flowers. One memorable occasion was
the 80th birthday party for the distinguished mathematicians
Fritz Hirzebruch
and
Sir Michael Atiyah, with their renowned Signature
Formula baked in bread by Ida and placed along the full length of
the table.

Andrew and Ida had one child Carla, who grew up in Edinburgh. In marrying Ida, Andrew also gained two teenage step-children, Matt and Alice, who stayed in America when Andrew and Ida moved to Edinburgh. Eventually Andrew had four American grandchildren, Emily, Christina, Michael, and Thomas, whom he loved and who all loved their “Grandrew”. Later his daughter Carla also had a child, his much beloved grandson Nico Marcel, who greatly enriched his final years.

Many thanks to Iain Gordon, Ian and Taida Hambleton, Anna McDuff, Erik Pedersen, Carla Ranicki, Carmen Rovi and Dennis Sullivan for their contributions to this tribute.