Periodic Points and Topological Restriction Homology

Malkiewich, Cary; Ponto, Kate

doi:10.1093/imrn/rnaa174

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…Remark These ‘cyclic’ versions of

prefixTHH

with coefficients have also appeared in the work of Lindenstrauss–McCarthy [12] and Malkiewich–Ponto [16]. …”

Section: Unwindingmentioning

confidence: 88%

Unwinding the relative Tate diagonal

Lawson

2021

Journal of Topology

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We show that a spectral sequence developed by Lipshitz and Treumann, for application to Heegaard Floer theory, converges to a localized form of topological Hochschild homology with coefficients. This allows us to show that the target of this spectral sequence can be identified with Hochschild homology when the topological Hochschild homology is torsion‐free as a module over prefixTHH∗false(F2false), parallel to results of Mathew on degeneration of the Hodge‐to‐de Rham spectral sequence. To carry this out, we apply work of Nikolaus–Scholze to develop a general Tate diagonal for Hochschild‐like diagrams of spectra that respect a decomposition into tensor products. This allows us to discuss the extent to which there can be a Tate diagonal for relative topological Hochschild homology.

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“…Remark These ‘cyclic’ versions of

prefixTHH

with coefficients have also appeared in the work of Lindenstrauss–McCarthy [12] and Malkiewich–Ponto [16]. …”

Section: Unwindingmentioning

confidence: 88%

Unwinding the relative Tate diagonal

Lawson

2021

Journal of Topology

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“…• Given a map of base categories H : T → S that strictly preserves products and Beck-Chevalley squares, and an smbf C → S, the pullback H * C → T has a canonical structure as an smbf. This can be generalized further, see [MP,Lemma 10.1].…”

Section: Grothendieck Fibrations and Constellationsmentioning

confidence: 90%

“…Inverting the stable equivalences gives a smbf hoS, whose tensor product is the left-derived external smash product, and whose Beck-Chevalley squares are the homotopy pullback squares. See [MP,Theorem 8.9] and [Mal].…”

Section: Grothendieck Fibrations and Constellationsmentioning

confidence: 99%

Coherence for indexed symmetric monoidal categories

Malkiewich¹,

Ponto²

2018

Preprint

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Indexed symmetric monoidal categories are an important refinement of bicategories -this structure underlies several familiar bicategories, including the homotopy bicategory of parametrized spectra, and its equivariant and fiberwise generalizations.In this paper, we extend existing coherence theorems to the setting of indexed symmetric monoidal categories. The most central theorem states that a large family of operations on a bicategory defined from an indexed symmetric monoidal category are all canonically isomorphic. As a part of this theorem, we introduce a rigorous graphical calculus that specifies when two such operations admit a canonical isomorphism.

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“…For k = 1, the fixed points of f can be eliminated equivariantly, therefore they can be eliminated on M H1 . (See, for example, Theorems 4.7 and 9.1 of [MP20]. )…”

Section: Isovariant Fixed Point Theorymentioning

confidence: 99%

Isovariant homotopy theory and fixed point invariants

Klang¹,

Yeakel²

2021

Preprint

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An isovariant map is an equivariant map between G-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein-Williams equivariant intersection theory for a finite group G. We prove that under certain reasonable dimension and codimension conditions on H-fixed subspaces (for H ≤ G), the fixed points of a self-map of a compact G-manifold can be removed isovariantly if and only if the equivariant Reidemeister trace of the map vanishes. In doing so, we build a new Quillen model structure on the category of isovariant spaces such that G-manifolds are both fibrant and cofibrant, yielding an isovariant Whitehead's theorem. In addition, we speculate on the role of isovariant homotopy theory in distinguishing manifolds up to homeomorphism.

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Periodic Points and Topological Restriction Homology

Cited by 4 publications

References 27 publications

Unwinding the relative Tate diagonal

Unwinding the relative Tate diagonal

Coherence for indexed symmetric monoidal categories

Isovariant homotopy theory and fixed point invariants

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